Cryptographic Engineering on COVID-19 Telemedicine: An Intelligent Transmission Through Recurrent Relation Based Session Key

Cardiac Related Works

Patients can avail their medical facilities from a distant place through electronic health services. The use of Internet based technology has reduced the recurrent hospitals visits post cardiac surgery [15]. It provides constant monitoring of patients’ health status and conditions from a remote place. Electronic telemedicine services are the emerging health care components when cardiac patients are facing difficulties during this COVID-19 crisis. Patients can manage and safeguard their health through online services [16]. The usage of Internet technology has offered to access and exchange medical data online anytime [17]. A device based integrated care component may be installed in patients suffering from myriad cardiovascular diseases. It may offer COPD patients a self-management approach. It may act as a measure before their treatments [18].

Hypertrophic Cardiomyopathy (HCM) [19] is related with thickening of the heart muscle, most commonly at the septum between the ventricles, below the aortic valve. This leads to thickening of the walls of the heart and abnormal aortic and mitral heart valve function, both of which may impede normal blood flow out of the heart. Hypertrophic cardiomyopathy (HCM) has no symptoms or only minor symptoms, and lives a normal life. Symptoms of HCM can occur at any age and may include chest pain, breathing shortness (dyspnea), fatigue, fainting (caused by irregular heart rhythms, abnormal responses of the blood vessels during exercise). Palpitations are caused due to abnormal heart rhythms (arrhythmias), such as atrial fibrillation or ventricular tachycardia.

Cardiology Telemedicine in COVID-19

Patients having co-morbidity in terms of cardiac complications are more prone to the novel coronavirus. Such patients require special attention through digital healthcare support system. Neubeck et al. [20] had reviewed some articles regarding the digital healthcare support to the cardiovascular diseases (CVDs) patients. They have tried to bring the evidence of digital healthcare support in this contemporary quarantine times and COVID-19 isolations. Bryant M.S. et al. [21] had reviewed the articles in context of the functioning of telehealth to the cardiopulmonary rehabilitation amid COVID-19 pandemic. Telehealth curtails the treatment time, cost, and physical travel for the patients. By using such services, geographical barriers are being diminished, else such patients would not be able to attend the hospitals physically due to various COVID-19 lockdown constraints. Peter R.J.G. et al. [22] had mentioned the importance of telemedicine on the cardiac rehabilitation patients in the period of coronavirus. Miller J.C. et al. [23] had surveyed the relevance of the smart devices used by the remote cardiac patients in this global pandemic crisis. Moreover, such patients were monitored through Remote Patient Monitoring (RPM) from their homes/quarantines from the heart perspectives. Chowdhury D. et al. [24] had provided a brief introduction of telehealth resource utilization in the view of pediatric cardiac unit. A rapid shift has been made in order to focus on the telehealth day to day services due to the COVID-19 social distancing and lockdown constraints.

Classical Cryptographic Engineering

Symmetric key cryptography can carry huge amount on data on any online transactions. Some of the common such algorithms are stated below.

Session Key Generation

Chen C.L. et al. [25] had proposed session key for the wireless sensory network communications. A secret key should be shared between the participating nodes for encryption purpose. They had designed dynamic key in order to reduce the intruding. Meena U. et al. [26] had designed a secured key agreement mechanism for the wireless transmissions. They had tried to abolish the data security challenges. Their technique involves fuzzy C means clustering and social spider optimization with low power consumption. Azarderskhsh R. et al. [27] had proposed a secured clustering technique based on deterministic pairing of public keys. Two nodes belonging to the same cluster will be able to establish a key pair without disseminating any further information to the remaining nodes. Their technique has shown terminal-to-terminal authentication, minimum memory space, and resistance to terminal attacks. Dwivedi R. et al. [28] had proposed a fingerprint basis biometric cryptographic mechanism for the secured data communication. They has used the person’s biometric trait to have the session key. Key leakage has been reduced. Sarkar A. et al. [29] had proposed a nature-inspired salp swarm based session key generation of 256 bits length for the transmission in E-health. Biometric traits were also included in their scheme for better patient data security. Sarkar et al. [30] had proposed a dynamic key generation scheme which works under the metaheuristic cuckoo search algorithm.

Secret Sharing

Secret sharing technique is used to divide the data by into multiple shares. And the original can be reconstructed only through minimum number of shares. Shamir’s secret sharing scheme is based on a polynomial function [31]. Blakey’s Secret Sharing Scheme has been used to solve secret sharing problem by the geometrical concepts [32]. Beimel A. et al. [33] had used multi-linear secret sharing concept on field elements. Sharing is done on random field secret elements and fixed field elements. Their technique seems to be very powerful on linear configurations. Sarkar A. et al. [34] had proposed soft computing on neural networks for the intraoral information sharing in the electronic medical field. Bhowmik A. et al. [35] had proposed a symmetric key based secret sharing of information. Their novel cryptographic technique defends against the intruders. Csirmaz L. et al. [36] had investigated the secret online sharing methods. Sarkar A. et al. [37] had used the gingival data transmission through secret sharing in the teledental domain. Their scheme has the resistance against the malicious attackers.

Proposed User-Defined Mask Generation Method

The mask matrix [40, 41] of the order n * ⁿC_k-1 has been called to generate the confusion matrices. The algorithm for said masking function is given below.

In the above algorithm, a mask matrix has been proposed. It comprised of n number of shares. The dimension of such matrix is given by n * ⁿC_k-1. A decrementing loop will be executed from ⁿC_k-1 to zero. In every iteration, the number of ones will be counted. Those satisfying with three will be selected for the mask matrix formation. At last, increasing sort will be done on the stored array. Finally, the matrix will be generated on the transpose operation itself for n number of recipients. In this COVID-19 telemedicine system, this matrix is used to generate the confusion matrix. Let n = 5, and k = 3, the mask matrix will look like as in the row-major format in the following Fig. 4.

For example consider a data (D) of ten bytes long be like $\mathit{COMSCMUCWC}$. The following Table 1 will provide the OR operation performed on the mask matrix of Fig. 1 and data (D).

The resultant individual shares will be of double length where first row is being attached first followed by OR operations of the above matrix, as given in the following Fig. 5.

It is very much obvious that each share will contain some missing bytes and those may be retrieved by accumulation of threshold k number of shares.

Proposed Session Key Generation Based on Recurrence Relation

Recurrence relation is defined as a sequence of linear function of earlier terms. There are two types of recurrence relations: a) linear recurrence relation, and b) linear non homogeneous recurrence relation [42].

Linear recurrence relation is a homogenous recurrence relation of degree $k$ with constant coefficients is of the form $b_n=d_1{b}_{n-1}+d_2{b}_{n-2}+\cdots +d_k{b}_{n-k}$, where $d_1,d_2,\cdots ,d_k$ are real numbers, and $d_k\ne 0$. $b_n$ is expressed in terms of the previous $k$ terms of the sequence. Let $b_n=d_1{b}_{n-1}+d_2{b}_{n-1}+\cdots +d_k{b}_{n-k}$ be an assumed linear homogeneous recurrence. It has been assumed that the sequence term $b_n$ satisfies the recurrence formula. Also the sequence term $b{\prime }_n$ satisfies the given recurrence formula. So,$p_n=b_n+b_n^{\prime }$ and $p_n=t{b}_n$ are also sequences that satisfy the recurrence, t may be any constant value.

Linear non-homogeneous recurrence is a non-homogenous recurrence relation [11] with constant coefficients is a recurrence relation of the form $a_n=d_1{a}_{n-1}+d_2{a}_{n-2}+\cdots +d_k{a}_{n-k}+g(n)$, where $d_1,d_2,\cdots ,d_k$ real numbers, and $g(n)$ is a function depending only on $n$. The recurrence relation $a_n=d_1{a}_{n-1}+d_2{a}_{n-2}+\cdots +d_{n-k}{a}_{n-k}$, is called the associated homogeneous recurrence relation. Here the concept of recurrence relation is used for random number generation that has been implemented for the session key generation in this paper. This novel idea of key generation is a unique concept in discrete mathematics [43, 44].

This module focuses on the process of session key generation for medical data encryption. This key is used in confusion matrix generation. Here the concept of non-homogeneous recurrence relation is used for the said key generation module. At first session key is XORed with symmetric key and then divide into $n$ number of shares using mask matrix and then each share of session key is transmitted to receiver end attached with each share of message.

The above mentioned algorithm 1.2 has described about the recurrence relation and session key generation from that recurrence relation. Session key means, it varies with times that is it may change with respect to time for medical transactions. We can generate different session key by changing different constant terms of recurrence relations. The application of recurrence relations in session key generation is a novel approach in this article.

Proposed Confusion Matrix Generation

The proposed technique implies XOR operation of each rows of the masked matrix on the cardiac report binary matrix. Confusion matrices will be thus generated before transmission in this corona virus pandemic time. The following algorithm will explain the concept of confusion matrix.

This algorithm 1.3 has shown how to create confusion matrix using session key and binary file. The concept of matrix operation has been used to create confusion matrix. Here bitwise XOR operation was used on mask matrix, session key and binary file. The number of rows and columns were taken from binary cardiac file. This matrix helps to increase the ambiguity in the proposed cipher text.

Proposed Encapsulation of Secret Shares

This sub-section deals with the encapsulation of the individual secret shares into a proposed shield structure of Head-Tail. An art of wrapping the secret shares into a different layered structured of single unit before the final departure of the shares in the wireless domain is done through this share encapsulation. Two different structures of head and tail are added at the front and rear of each share respectively. It is deliberately done to make the secret shares more protected against the task of intruding. The following Fig. 6 represents the block diagram of the said concept.

In this paper we have used a frame format for shared message transmission. This frame format is created using algorithm 1.4. Here header and tailer part is created using session key1 and session key2. 2nd column elements are taken from session key2 and are used in the creation of tailer.

Case of Histogram Analysis

The clinical signal online database has been used in this study for different sets of tests to establish its efficiency and effectiveness [45]. Histogram analysis has been carried out at this proposed technique. How binary values of 1 s and 0 s of a cardiac report are spread, this has been studied. A graphical representation of frequency distribution inside the cardiac file has been shown in following Fig. 4. The distribution of data i.e. peaks; spreads and symmetricity is not relevant. The peaks bars represent the maximum occurrences and spreads represent the information variation. The results as per histogram obtained at the following Fig. 8 are neither skewed and nor well distributed.

Different cardiac reports were analyzed in this proposed technique with such extensions likes of.pdf,.txt,.doc, etc. This technique is valid in telemedicine systems that between threshold numbers of doctors, the original patients’ cardiac file cannot be generated [46]. So the confusion matrices are more intelligent enough to make the intruders fool. Each confusion matrix is nothing but a double dimensional matrix of 1 s and 0 s. Only the valid doctors can open the file that is needed for patients’ treatments. Thus, the proposed confusion matrix generation technique may be accomplished as a COVID-19 Telemedicine.

The bar graphs observed in the above Fig. 8 are not appropriate in terms of patients’ data security. However, the fruitfulness of the proposed technique in terms of histogram in given in the later sub-Sect. 10.4.

Case of Autocorrelation Analysis

Analysis of autocorrelation of different types of source files was carried out in this paper. Autocorrelation of a plain file is an index of the similarity at various levels. Autocorrelation of source file without encrypting through proposed technique is given at the following Fig. 9.

From the above figure, it can be said that there exists similarities in the characters inside the source file. Moreover, the utility of the proposed cryptographic technique is illustrated in the later sub-Sect. 10.4.

Case of Floating Frequency Analysis

In this sub-section, the analysis of floating frequency of the source files was carried out. The local information content inside the file is shown here in graphs. It means how many varieties of sixty four characters are present in the source medical file. Figure 10 shows the floating frequencies of the same file without any proposed encryption.

The robustness against the intruders of the proposed method is mentioned in the later sub-Sect. 10.4.

Contrast in Terms of Histogram, Autocorrelation, Floating Frequency

In the following Table 2, there has been the histograms, autocorrelations, and floating frequencies of the same source file for n number of secret shares. These graphs were derived when encrypting the file with the proposed technique.

The above stated histograms, autocorrelations, and floating frequencies of the secret shares developed by proposed methodology are showing equivalence distribution of the data of a shared cardiac source file. This proves the robustness of the proposed technique in this global pandemic. This cryptographic method on heterogeneous reports safeguards the different Man-in- the middle attacks [47, 48]. Intruders will get no clues from the generated cipher texts inside the wireless networks.

Correlation Analysis

In this sub-section, the correlation between ASCII difference and total number of changed characters has been carried out on different sets of cardiac files. A secured cryptographic engineering technique should transform a text file (.pdf,.docx,.txt,.xls, etc.) into a randomized encrypted file with low correlation. The formula for Pearson correlation coefficient [48] is given at the following Eq. 1.

Here, $r_{\mathit{cor}}$ means the coefficient of correlation, $x_i,y_i$ are the values of x and y in the data file respectively, $x^{\prime }$, $y^{\prime }$ are the average of x and y data respectively. The rule of thumb which is used to draw the impact in this respect is given at the following Table 3.

The above stated table contains the different ranges of the correlation coefficient values and its impact. The correlation values are given below at the Table 4, when computed on different heterogeneous files. The significance of the session key may be drawn from the following table.

The above stated tables contains the headers as Name of Input(s), SD of X Values, SD of Y Values, Correlation Coefficient(r), Coefficient of determination, Significance of Test Value, and Standard error slope values. Here X and Y denote the number of changed characters and ASCII differences respectively. The Pearson correlation coefficient gives the strength and course of the straight connection between two factors. From the above Table 2 it has been seen that the estimation of correlation coefficient among X and Y is − 0.362 which is less than 0.0. This shows that there is a solid negative connection between the factors or the factors may have a nonlinear relationship. The relationship is negative in light of the fact that, as one variable expands different abatements [38]. In any case, from the disperse plot given in Fig. 11. There is nonlinear relationship exists between two factors (X, Y) from the above presented table.

Chi-Square Context

The contrast between the noticed recurrence of characters and the genuine recurrence of characters is known as Chi-Square test. Individual Chi-Square computations were made on the different shares as generated by the proposed technique. The Eq. 2 shown below performs the said computation.

where, $OF{C}_i$ and $AF{C}_i$ means the existing occurrence and the contemplated occurrence of ith character respectively in the share.

The above stated Table 5 is comprised of the following table headers as Source File Name, Secret Share Number, and Proposed Secret Share. It may be stated that the proposed technique of secret sharing based on recurrence relation for COVID-19 transmission provides good quality of cryptographic encryption in terms of Chi-Square values.

Statistical Strength of Session Keys

NIST Test Suite [49] is a statistics package comprised of fifteen tests. Its objective is to determine the randomness of recurrence relation session key proposed in this paper. Robustness of the session key is determined by these tests. Six different category source files were tested through seventy five set of session keys. Average values are being noted in the following Tables 7, 8, 9, 10, 11 and 12 as per our simulations done. The accompanying Table 6 is the list table of the fifteen measurable statistical tests.

The NIST test suite has been comprised of fifteen in-built statistical tests. In order to prove higher robustness of our proposed session key, we have used those fifteen tests. For our convenience, such fifteen tests have been renamed as TEST@01, TEST@02, …, TEST@15, as stated in the above Table 6. All fifteen tests were successfully conducted on our proposed scheme. No limitations on the test numbers were done here.

The above stated Tables 7, 8, 9, 10, 11 and 12 contain the table headers as Test Code, Session Key with p-value >  = 0.05, Percentage and Outcome.

Patients’ Data Security Analysis

This sub-section explains the security of the medical data in this COVID-19. Recurrence relation based sesion key has been generated for the cryptographic engineering domain. The use of proposed confusion shares had redued the chances of stealing from different unknown malicious agents. Different types of attacks on the patients’ confidential data against the proposed system have been briefly stated.

• Dos Attacks on Patients’ Data: In this proposed strategy, the fractional mystery portions of the COVID-19 telemedicine was dispersed to all the partaking machines inside the gathering of known users. An indepndent hub has no advantage to remake the information without collaboration from the others. Consequently, the remaining task at hand of every hub has been diminished. Accordingly, the proposed method can effieciently withstand Dos assaults under such COVID-19 telemedicine.

• Mid-way Intervene Attacks on Patients’ Data: Insightful transportation systems were conveyed in this proposed strategy of recurrence relation based session key in COVID-19. The sent information might be meddled by the outer intruders. The proposed COVID-19 telemedicine do opposes against the impedance assaults. The session key that was generated here have been tried to detect under various statstistical properties [50, 51]. But the results were failed to its strong efficiency.

• Replay Attacks on Patients’ Data: This proposed method can oppose against the replay assault by the intruders. Since the cardiac reports was broken and scrambled into fractional offers, at that point it would not be conceivable to recover except if the edge shares are being summarized. That implies no single hub contains all the information. In the event of hub being compromized, the misfortune the information burglary has been checked here strongly.

• Man-in-the Middle (MITM) Attacks on Patients’ Data: As a foe segment, gatecrashers are dynamic to take those patients' significant information inside the organization. To unscramble the information, gatecrashers need all the minimum number of offers to uncover the data. Yet, this would not be possible because of the quantity of partaking and threhols shares are kept covered up.

• Session Key Fitness: The session key has been generated through recurrence relation and ships off all the partaking hubs in a similar gathering of known users. Before that it has been checked by the NIST suite [49]. Thus, this proposed method guarantees genuine haphazardness in the session key.

In comparison with the previous works, the proposed technique has better efficacy in terms of the patients’ data security. Chen C.L. et al. [25] had not compared their technique on data security. But our technique has been tested under the NIST suite for the proposed set of session key. The proposed p-values are within the normal limits as shown in the above sub-section.

Brute Force Attacks

Efficient management of key space makes the brute force attack [46] infeasible. In this attack, attacker tries to translate the cipher text into plain text using every possible key. On average, half of all possible keys are enough for achieving success. Algorithms are known to all in most networking system but brute-force attack will impossible if the algorithm uses large key space. Presently, the fastest super computer is Japan's Fugaku having speeded $415.53petaflopsi.e.415.53x{10}^{15}$ floating point operations per second. Let us consider each trial requires 2000 FLOPS to complete one check. So number of trials complete per second is: $207.77x{10}^{12}$. The quantity of seconds in a year is:$365\ast 24\ast 60\ast 60=31,53,600sec$.

Now from the above stated key space the formula for breaking the session key is $2^C÷\left(207.77\ast {10}^{12}\ast 3153600\right)=Y;$ where $Y$ denotes number of years required. When $C$ increases then Y increases i.e. (C $\infty Y$), where C is the session key length. Thus for large key length it is very difficult to decode the session key. A cipher text with such a long key space is sufficient for reliable practical use in this corona virus era. It proves that a session key is good enough to overcome the brute force attack due huge computation time needed. Meena U. et al. [26] had tried to demolish the data security challenges. But they had not worked on Brute-Force attacks. In this paper, Brute-Force attack has been considered with the proposed recurrence relation based session key. More compatible security efforts are bare minimum requirements in any cryptographic system [52]. Hence it would be very efficient in developing the COVID-19 telemedicine where patients’ confidentiality is an integral factor.

Differential Attacks

Intruders comprehensively endeavor to derive any sort of heuristics between the proposed cipher text and unique cardiac files. The set of seventy five session keys generated through proposed recurrence relation were tested under the differential attacks. A flip in the session key would incredibly change the entire composition of the cipher text. Thus, intruders are not in a good position for correct predictions. The following Table 13 contains the randomized sampling done for this purpose. The length of recurrence relation session key is 128, which is further used as AES encryption in the COVID-19 telemedicine. The following table has been done on an arbitrary message of nominal size. There exists a frequency of keys extracted according to the flips occurred in the bits positions.

The above mentioned Table 13 is composed by the following table headers as Range of bit position (Class Interval), Total No. of Keys (Frequency), and Affected No. of bits on cipher text. Graphical representation of the above stated table has been made at the following Fig. 12.

The above stated graph of Fig. 12 shows the differential attacks on the proposed COVID-19 telemedicine. When compared to other works, this work has gained its positivity. Sarkar et al. [29] has not considered differential attacks on their proposed biometric key. But in this paper, we have shown the differential attack, and its resistance against such attack.

Analysis of Entropy

Entropy of a cardiovascular report file is the degree of distribution in terms of 256 ASCII characters. Generally in ordinary file, it doesn’t contain all 256 characters at uniform distribution. The proposed encryption transforms the highly appeared characters to sparsely appeared characters at random. The following Table 14 shows the entropy of the cardiovascular modules prior and post encryption. After encryption the entropy value is approaching the maximum limit of eight, which is acceptable.

The entropy graph on different set of files based on the above table is shown in the following Fig. 13.

The entropy post encryption has been computed as average values of all the shares. From the above mentioned figure it can be concluded that the proposed encryption has yielded much higher results if compared with pre-encryption.

Cryptographic Time

Using the proposed cryptographic technique on COVID-19 telemedicine, the transmission of the medical data, clinical reports, and prescriptions is possible to the physicians through online mode. The cryptographic time needed is another crucial index towards the effectiveness of the proposed technique [39]. It includes both the encryption time and decryption time. Six different source files were encrypted through proposed set of seventy five session keys one by one. The following Table 15 contains the average cryptographic time for the said files.

The above stated Table 15 contains the following table headers as Sl. No., File No., Encryption Time (ms), Decryption Time (ms), Total Cryptographic Time (ms), and Average Cryptographic Time (ms). The average cryptographic time of the proposed engineering technique has been noted in the last column, which is acceptable.

In the next Table 16, a comparison has been exclusively made with respect to the existing cryptographic methods. Six input files of heterogeneous data were considered here. The proposed technique on COVID-19 telemedicine has performed with better outputs.

In the following Figs. 14, 15 and 16, a comparison graphs were plotted on the proposed technique with respect to classical techniques. Initially, the encryption graphs were drawn at the following Fig. 14.

Then, the decryption graphs were drawn at the following Fig. 15 on the data cited at the above Table 16.

Finally, the cryptographic graphs were plotted at the following Fig. 16 on the same data that has been mentioned at above Table 16.

All the above stated graphs at Figs. 14, 15 and 16 have close par performance to the existing encryption techniques. This proves the efficacy of the proposed cryptographic technique on COVID-19 telemedicine.

Time Complexity Evaluation of the Proposed Technique

The time complexity of any software is a vital aspect for its acceptance. In the sub-section, the time complexity of the proposed cryptographic method has been generated. This method has been divided into six modules, namely, Recurrence Session Key Generation, Mask-Generation, Binary File Conversion, Partial Encrypted Share Generation, Share Encapsulation, and Final AES Encryption. The individual time complexity of each module has been written in the following Table 17. By summing up, the overall time complexity of the proposed method can be evaluated.

Conflict of interest

The author declare that they have no conflict of interest.

Ethical Approval

This article does not contain any studies with human participants or animals performed by any of the authors.